Cell Motility and the Cytoskeleton 1855-62 (1991)

Dilution-Induced Disassembly of Microtubules: Relation to Dynamic Instability and the GTP Cap William A. Voter, E. Timothy O’Brien, and Harold P. Erickson

Department of Cell Biology, Duke University Medical Center, Durham, North Carolina Microtubules were assembled from purified tubulin in the buffer originally used to study dynamic instability (100 mM PIPES, 2 mM EGTA, 1 mM magnesium, 0.2 mM GTP) and then diluted in the same buffer to study the rate of disassembly. Following a 15-fold dilution, microtubule polymer decreased linearly to about 20% of the starting value in 15 sec. We determined the length distribution of microtubules before dilution, and prepared computer simulations of polymer loss for different assumed rates of disassembly. Our experimental data were consistent with a disassembly rate per microtubule of 60 p d m i n . This is the total rate of depolymerization for microtubules in the rapid shortening phase, as determined by light microscopy of individual microtubules (Walker et al.: Journal of Cell Biology 107:1437-1448, 1988). We conclude, therefore, that microtubules began rapid shortening at both ends upon dilution. Moreover, since we could detect no lag between dilution and the onset of rapid disassembly, the transition from elongation to rapid shortening apparently occurred within 1 sec following dilution. Assuming that this transition (catastrophe) involves the loss of the GTP cap, and that cap loss is achieved by the sequential dissociation of GTP-tubulin subunits following dilution, we can estimate the maximum size of the cap based on the kinetic data and model interpretation of Walker et al. The cap is probably shorter than 40 and 20 subunits at the plus and minus ends, respectively. Key words: purified tubulin, computer simulations, polymer loss

INTRODUCTION “Dynamic instability” refers to the complex reactions of assembly and disassembly of microtubules that have been described recently in vitro [Mitchison and Kirschner, 1984a,b; Horio and Hotani, 1986; Walker et al., 19881 and in vivo [Schulze and Kirschner, 1986; Sammak et al., 1987; Cassimeris et al., 19881. Each end of a microtubule can exist in one of two phases. At concentrations of free tubulin near that of steady state, the majority of microtubules are in the “elongation” phase, and continue growing at a slow, steady rate. A smaller fraction of microtubule ends are in a phase of “rapid shortening,” depolymerizing at a rapid rate. Transitions between the two phases occur abruptly, stochastically, and infrequently. The transition from the elongation phase to rapid shortening is termed “catas0 1991 Wiley-Liss, Inc.

trophe. The transition from rapid shortening to elongation is called “rescue.” (Note that some laboratories have used the term “catastrophic disassembly” to refer to microtubules shortening to completion, without rescue. We have preferred to use the single word “catastrophe” for the abrupt and dramatic transition from elongation to rapid shortening [Walker et al., 19881.) The most attractive model explaning dynamic instability is the GTP cap, originally proposed by Carlier and Pantaloni [1981] and Mitchison and Kirschner [ 1984a,b]. Hydrolysis of GTP is postulated to lag behind the association of subunits into a growing microtubule, ”

Received April 3, 1990; accepted September 13, 1990. Address reprint requests to Harold P. Erickson, Dept. of Cell Biology. Duke University Medical Center, Durham, NC 27710.

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maintaining a cap of GTP-tubulin subunits at the growing end, and a core of GDP-tubulin subunits in the interior. The GTP cap is postulated to stabilize the end of the microtubule and favor continued growth (elongation phase). The GDP core is postulated to be highly unstable, resulting in rapid depolymerization if it is exposed. A crucial assumption in this model is that disassembly can occur only from the exposed end; thus even a very small GTP cap at each end can stabilize the entire microtubule. Catastrophe is thought to involve the loss of the GTP cap, the specific molecular event being the loss of the last GTP-tubulin subunit. If the cap is larger than a single subunit, it may grow and shrink stochastically in a balance of three reactions: 1) assembly of new GTP-tubulin subunits onto the growing end increases the cap; 2) dissociation of GTP-tubulin subunits from the growing end decreases the cap; and 3) hydrolysis of GTP also decreases the cap. Quantitative data on the first two reactions have been obtained by video microscopy of single microtubules [Walker et al., 1988; O'Brien et al., 19901. The mechanism of GTP hydrolysis is not known, and consequently the size of the GTP cap and a complete model for its dynamics cannot yet be specified. We have argued that hydrolysis must be coupled to assembly to limit the cap to a very small size [O'Brien et al., 1987, 1990; Walker et al., 19881. A recent study by Stewart et al. [ 19901 has provided additional evidence for coupled hydrolysis and a very small cap. The kinetic constants for the reactions involved in dynamic instability, as determined by Walker et al. [ 19881, are summarized in Table I. These values will be discussed later, but we want to call attention here to the large difference in dissociation of subunits from the GTP cap vs. the GDP core (k-," = 44 and 23 s-' from the plus and minus ends, vs. kkIrs = 733 and 915 s-'). Because of this large difference in dissociation rates, measurements of disassembly following a rapid dilution can give information on the size of the GTP cap. Following dilution, subunits should first dissociate relatively slowly from the GTP cap, and then dissociate very rapidly as soon as the cap is gone. Ideally, one would like to observe single microtubules, to see how soon catastrophe occurs following a dilution. Recent experiments using a flow cell with the video-enhanced light microscope reported a lag of several seconds between dilution and catastrophe [Walker et al., 1989, 19911. A limitation in these experiments is that dilution depends on the flow and mixing characteristics of the chamber, requiring several seconds to achieve a -7-fold dilution. The approach we take in the present study is to observe the disappearance of total polymer in a bulk solution following dilution. The advantage is that full

TABLE I. Kinetics of Dynamic Instability From the Data of Walker et al. [1988]* k,e k,'-C, k- l e kh(@C,) k- ,r'

Plus end

Minus end

8.9 62.3 44. 18.3 133.

4.3 30. I 23. 6.9 915.

(pM-I s-') (S-I)

(S-I) (S-I) (S-I)

*k2e is the second-order rate constant for addition of subunits to the end of the microtubule (cap). k,'.C, is the pseudo-first-order rate constant for addition of subunits to the cap, at the steady-state free subunit concentration of 7 p M . k- l e is the first-order rate constant for the dissociation of subunits from the cap during elongation. kh(@C,) is the rate of hydrolysis at steady state, calculated as the difference between k,'C, and k k I e . This is not a rate constant, and implies nothing about the mechanism of hydrolysis, since it is simply a calculated rate at a single subunit concentration (7 pM). kkIrs is the first-order rate constant for dissociation of subunits during rapid shortening (from the GDP core).

dilution is achieved in less than 1 sec, and polymer can be measured at 1 sec time intervals. If one knows the concentration of microtubule ends and the distribution of lengths, the rate of loss of bulk polymer can be translated into an average shortening rate per microtubule. Such a study has already been done by Karr et al. [ 19801. However, their experiments were performed with tubulin co-assembled with microtubule-associated proteins (MAPs), or with purified tubulin assembled and diluted in 3.4 M glycerol. Both MAPs and glycerol significantly modify the kinetics of microtubule assembly. MAPs eliminate or greatly reduce the excursions characteristic of dynamic instability [Horio and Hotani, 19861, and these excursions have never been reported in glycerol buffers. We therefore thought it important to repeat these measurements in a buffer that is known to support dynamic instability, and to correlate measurements of dilution-induced disassembly in bulk solution with the kinetic parameters of dynamic instability determined for single microtubules. MATERIALS AND METHODS Tubulin Purification

Tubulin free of microtubule-associated protein was prepared from porcine brains as described previously [Voter and Erickson, 19841 and was stored at -80°C in 3.4 M glycerol. Some days or weeks before use, the tubulin was transferred into P-buffer (PIPES buffer-I00 mM PIPES, pH 6.9, 2 mM EGTA, 1 mM MgSO,, and GTP at 0.1, 0.2 or 1 .O mM) by assembling microtubules (adding MgSO, to 5 mM and warming to 37°C) and continuing through a full cycle of assembly, centrifugation at 37"C, followed by a cold centrifugation. The tubulin was then passed over a small Sephadex G-25 col-

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at time zero was determined separately by simultaneous dilution and fixation of the starting steady-state microtubules. The rack containing the test tubes was shaken vigorously in a circular motion at about 5 cycles/sec. The Assay of Microtubule Disassembly temperature of the dilution buffer, glutaraldehyde, and Microtubules for disassembly experiments were microtubules was maintained at 37°C in a large water prepared by warming 25 to 30 p M tubulin in P-buffer for bath. Within a few minutes after fixation, the microtua few minutes and then seeding the assembly adding 1% bules were centrifuged at room temperature and the suby volume microtubules assembled in a magnesium- pernatants were analyzed for protein by the Bradford glycerol buffer system. After a few minutes incubation assay (Bio-Rad Labs.) using purified tubulin as a stanthe microtubules were sheared by several passes through dard (A,,, for 1 mg/ml = 1.19 [David-Pfeuty et al., a 1.5 inch-long 22 gauge needle. After 15 to 40 min and 19771). The glutaraldehyde did not interfere with the either 3.5 or 5 min before the dilution, the microtubules protein assay. Microtubules were prepared for length measurewere sheared again. Two methods were used to monitor the amount of ment and counting essentially as described by Mitchison polymer remaining during disassembly: turbidity, and and Kirschner [ 1984al. The microtubules were diluted pelleting of microtubules after glutaraldehyde fixation. and fixed at the same time by adding 1 volume of miIn both procedures the total polymer before dilution (the crotubules to 29 volumes of 0.83% glutaraldehyde in zero-time point) was determined by sedimenting a sepa- P-buffer, without GTP. After further dilution, the microrate, undiluted sample at 37°C. The concentration of sol- tubules were pelleted onto Formvar-coated grids and rouble tubulin in the supernatant was typically around 12 tary shadowed with platinum-carbon. The microtubules pM, consistent with a steady-state concentration of 7 were measured on prints made from electron microp M active tubulin, and 10-25% inactive protein, as de- graphs by using a Numonics 1224 electronic planimeter. termined in more detail previously [Walker et al., 19881. Turbidity was recorded at 350 nm in a Shimadzu UV-240 recording spectrophotometer equipped with a RESULTS tempcrature-controlled cuvette holder maintained at In order to study the disassembly of microtubules 37°C. A 4 mm-wide cuvette with 10 mm path length was usually used. To mix the microtubules rapidly into the following rapid dilution, it was first necessary to demcontents of the cuvette (for rapid dilution experiments) a onstrate that the dilution and mixing procedure did not in small mixing device was fabricated, consisting of a thin itself disrupt the microtubules. As shown in the first plate of polyethylene approximately 3 by 7 mm, with a section of Figure 1, microtubule assembly proceeded handle such that the plate could be suspended horizon- slowly after addition of seeds, but was greatly accelertally in the cuvette. The typical mixing procedure was to ated by shearing (at 10 min). Presumably, shearing fragadd 50 p1 of microtubules to the cuvette containing 700 mented the microtubules and multiplied the number of pl of buffer or soluble tubulin in buffer. A prewarmed seeds. Following this shear, a stable plateau of turbidity plastic pipet tip with the tip cut off to prevent shearing of was obtained by about 20 min. These steady-state mithe microtubules was used for the transfer. The mixer, crotubules were then subjected to the standard mixing which had been previously placed in the cuvette, was procedure, without dilution or addition, in which an inthen moved up and down twice and then removed from sert was moved down and up through the liquid in the the cuvette, and the cover was closed. About 3 to 4 sec cuvette. The mixing caused a small rise in turbidity, was required for the mixing procedure and the start of which relaxed to the plateau value in a few minutes (Fig. 1, middle section). If the mixing had sheared the microrecording. The amount of polymer was also determined at tubules, we would expect the turbidity to drop (see several time points by rapidly fixing with glutaralde- below). The small rise in turbidity probably reflects a hyde. An eight channel pipettor (Titertek, Flow Labs, disruption of ordered domains of microtubules [Hitt et Inc.) was used to dilute microtubules simultaneously in al., 19901. A similar transient rise in turbidity was seen eight 16 by 100 mm glass test tubes. At various times with the alternative mixing procedure (Fig. 1, right secafter the dilution, an equal volume of 1.67% glutaralde- tion, 8 min). To demonstrate the effect of more violent hyde (EM grade from Electron Microscopy Sciences, mixing, the steady-state microtubules were forced Inc.) in P-buffer without GTP was rapidly squirted into through a 22 gauge needle (Fig. 1, right section, 0 min). the test tubes from disposable plastic transfer pipets that As expected for fragmented microtubules, the turbidity had been previously placed in the test tubes, but sup- dropped significantly, and then rose again to the plateau ported with the tip above the liquid surface. The polymer value in about 2 min. Since the mixing procedures proumn (PD- 10, Pharmacia) that had been equilibrated with P-buffer with 0.1 or 0.2 mM GTP. Small aliquots were frozen and stored at -80°C until use.

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TIME (min 1 Fig. 1. Tests of the mixing and shearing procedures. Microtubule assembly was monitored turbidimetrically at 350 nm. The first section shows the assembly of prewarmed tubulin, which was seeded at 2-3 min, and sheared by six passes through a 1 .S inch 22 gauge needle at 10 min. Assembly accelerated and reached a plateau by 20 min. After several minutes the mixture was subjected to two episodes of mixing, at 0 and 8 min, center section. The mixing produced a small rise in turbidity, which relaxed to its previous value in a few minutes. The

duced no drop in turbidity, we conclude that they did not cause a significant fragmentation of the microtubules. Figure 2 shows the decrease in turbidity following a 15-fold dilution of microtubules (solid line). The microtubules had been grown to steady state, and then sheared 5 min before the dilution to obtain a more uniform and reproducible distribution of lengths. Upon dilution the turbidity drop was rapid and linear for the first 15 sec, and then slowed somewhat. Disassembly was virtually complete in 30 sec. To check that the turbidity was accurately reflecting the amount of polymer, a separate experiment was done in which small samples were removed at 5 sec intervals and assayed for polymer by fixing with glutaraldehyde, centrifuging, and assaying the supernatant for protein. Although there was some scatter in the data for the last 20-30% of dissassembly, for the first 15 sec following dilution this assay showed a linear drop in polymer that was virtually identical to the turbidity curve (data not shown, but see Fig. 3 for similar assay). To interpret the depolymerization curve in terms of kinetic constants for individual microtubules, we determined the number and length distribution of the microtubules at time zero, as described by Mitchison and Kirschner [1984a]. The length distribution is shown in the inset in Figure 2. The total mass of polymer was calculated by determining the total length of microtubules per unit area of grid surface, and assuming that all

microtubules were then subjected to shearing, at 0 min, right section. Turbidity dropped substantially and then rose again to the plateau value in about 2 min. At 8 min the microtubules were subjected to mixing by alternative procedure (microtubules were removed from the cuvette, mixed by swirling in a warmed test tube, and returned to the cuvette). The small rise in turbidity and relaxation were similar to the mixing in the center section.

TIME ( s e c s ) Fig. 2. Microtubule disassembly induced by rapid dilution. Microtubules were assembled from tubulin at 25.3 p M and, S min after the second shearing, were rapidly diluted IS-fold. The total polymer at time zero was determined by centrifuging a parallel sample prior to dilution and determining the protein in the supernatant. The thick line is the A,,, nm recording, scaled to intersect the 0.88 p M zero-time polymer. The other lines represent computer simulated microtubule disassembly, based on the distribution of lengths determined by electron microscopy (histogram inset), and assumed shortening at 25, SO, or 100 pm/min for each microtubule. The experimentally observed disassembly is somewhat faster than the computer curve for SO k m / min.

Dilution-Induced Microtubule Disassembly

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TIME ( s e a ) Fig. 3. Time course of rapid dilution-induced disassembly measured by glutaraldehyde fixation and pelleting of microtubules. The microtuhulrs were sheared and allowed to regrow for 5 min prior to dilution. The total tubulin concentrations were 26.4 p M and 24.0 p M for the upper and lower curves respectively. Dilutions were 15-fold into buffer using the eight-channel pipettor as described in Materials and Methods. The polymer values were calculated from the supernatants of the glutaraldehyde-fixed dilution samples. For the zero time point the sample was diluted directly into glutaraldehyde. The straight lines are least square fits to the data points.

of the microtubules in the diluted sample were deposited on the grid by the centrifugation. The total polymer calculated from this quantitative electron microscopy was about 70% of that determined by assay of protein in the pellet and supernatant. Given the possible errors in each of the several steps in this assay, we consider this agreement quite good. The important parameter for our analysis is the relative distribution of microtubule lengths. The length histogram shows approximately equal numbers of microtubules for the first six length intervals, out to 30 pm length, and few microtubules longer than 3540 pm. The experimental turbidity curve was then simulated by a simple model, using the values in the histogram for the distribution of microtubules of different lengths. For this initial modeling we assumed that all microtubules began rapid disassembly at a constant rate at the instant of dilution. This is essentially the same analysis used by Karr et al. [ 19801. A more complex analysis would have been required if there were evidence

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for a lag in loss of the GTP cap, but this simplest model fit the data quite well. We computed the disassembly rates for three assumed rates of shortening, 25, 50, and 100 p m per min per microtubule. We chose these values to bracket the rates of rapid shortening measured by Walker et al. [ 19881: 26 and 34 pm per min at the plus and minus ends gives a total disassembly of 60 pm per min. Our experimental curve in Figure 2 is closely fit by, but somewhat faster than, the computer-simulated curve for a total shortening of 50 pm per min per microtubule. The total shortening rate of 60 pm per min, which is predicted for rapid shortening at both ends, would fit our experimental disassembly curve quite well. The simulated curve calculated for 25 pm per min, which we would expect if microtubules were shortening from only one end, clearly does not fit our data. The assumption that disassembly begins immediately after dilution was consistent with the experimental data, but was only as precise as our earliest time points, about 3-5 sec in Figure 2. Moreover, the zero-time turbidity, immediately following dilution, is unknown. Although turbidity is a reasonably good measure of polymer over a limited range of concentrations, the turbidity following a 15-fold dilution is not simply related to the turbidity before dilution [Hitt et al., 19901 (our unpublished observations). In order to look for a lag in the onset of rapid disassembly, which would correspond to the time for caps to be lost, we developed an assay that would measure total polymer at time zero and at early time points following dilution. To obtain data at early time points we constructed an apparatus that allowed eight samples to be diluted at the same time, and stopped by 1:l dilution with fixative at 1 sec intervals. The samples were kept at 37°C and mixed gently during disassembly and fixation, as described in Materials and Methods. The polymer at time zero (before dilution) was determined separately. The results of two such experiments are shown in Figure 3. The polymer decreased linearly for 10 to 14 sec, and this line, extrapolated back to time zero, is very close to the total polymer determined before dilution. Because of the scatter in the data, we cannot exclude a lag of up to 1 sec before the start of depolymerization: i.e., the zero-time polymer value would fit the curve just about as well if it were maintained out to 0.5-1 sec. A lag of 2 sec is excluded by the data points at 2 sec, both of which are significantly below the zero polymer values and are on the line through the rest of the data. We conclude that rapid disassembly is initiated at each end within 1 sec following dilution. The rate of disassembly as measured by the turbidity assay (Fig. 2) was reproducible when this experiment was repeated with different tubulin preparations. This

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implies that the distribution of lengths is also reproducible, provided the tubulin concentration and the time between shearing and dilution is the same. To test the effect of time after shearing, we repeated the experiment in Figure 2, diluting the microtubules at 3 1/2 min rather than 5 min after shearing. In this case the distribution was shifted slightly toward shorter microtubules, the average length being 16.2 pm compared to 19.9 pm for Figure 2. The experimental disassembly rate was slightly faster than in Figure 2, as expected for the larger number of shorter microtubules. The computer simulation based on this length histogram fit the experimental curve well for disassembly at 50-60 pndmin, essentially the same as in Figure 2. Although the main point of the experiment in Figure 3 was to examine the very early time points not accessible in Figure 2, it is worth noting the general agreement of the disassembly rates measured by the two techniques. It should first be noted that both samples were diluted 5 min after shearing, and the lower curve in Figure 3 is at the same concentration as the sample for Figure 2, 13.5 p M before dilution. Therefore, the distribution of lengths in the starting solution should be about the same in each experiment. The disassembly curves are approximately linear out to 10 sec, from which an initial disassembly rate can be stated. The disassembly rates for Figure 2 and for the lower curve in Figure 3 are 0.057 and 0.047 pM/sec, a difference of only 20%. Our confidence in the 60 pndmin rapid shortening rate determined from our computer curve fitting is within a similar range, 2 20%.

DISCUSSION The goal of our study was to determine if dilutioninduced disassembly of total microtubule polymer, measured by bulk solution methods, could be interpreted in terms of the data for dynamic instability of single microtubules. The relevant kinetic constants measured in Pbuffer by Walker et al. [1988] are presented in Table I, lines 1, 3, and 5. In the present study we start with microtubules at steady state in the P-buffer, in which steady state free tubulin is 7 pM. (This is the concentration of soluble and active tubulin at steady state, as determined by protein assay following centrifugation, [Walker et al., 19881.) The rates on lines 2 and 4 are given specifically for 7 pM free tubulin. The most important kinetic parameter for our analysis is that of rapid shortening. The values of 733 and 915 s-' (26 and 34 pm per min) were determined by Walker et al. for the plus and minus ends of individual microtubules in the phase of rapid shortening. Our experimental depolymerization curve was slightly faster than a theoretical curve calculated for all microtubules

disassembling at 50 pm/min, and would correspond closely to a total shortening of 60 pm/min from both ends. This correspends well to the sum of rapid shortening rates observed for single microtubules. Moreover, this maximum disassembly rate was observed with no detectable lag following dilution. If there were a GTP cap of substantial size at the ends of the microtubule, we would have expected to see two phases in the disassembly curve. The first phase, which would persist until most microtubules had lost their cap, would have been a slow disassembly of subunits from the GTP cap. Only when a large fraction of microtubules were uncapped would disassembly accelerate to the full rapid shortening rate. Since we could detect no lag (